NMR (Nuclear Magnetic Resonance Spectroscopy) Literature / background (already in Stine) • Ferentz, A.E. and Wagner, G., Q. Rev. Biophys, 33, 29-65 (2000) – in Stine Current standing • ≈ 11 % of current structures solved by NMR (10 618 structures, 9287 proteins) • about 1/4 of smaller structures (<100 residues) Andrew Torda, Wintersemester 2015 / 2016, GST Andrew Torda 26/10/2015 [ 1 ]
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
NMR (Nuclear Magnetic Resonance Spectroscopy)
Literature / background (already in Stine)
• Ferentz, A.E. and Wagner, G., Q. Rev. Biophys, 33, 29-65 (2000) – in Stine
Current standing
• ≈ 11 % of current structures solved by NMR (10 618 structures, 9287 proteins)
• about 1/4 of smaller structures (<100 residues)
Andrew Torda, Wintersemester 2015 / 2016, GST Andrew Torda 26/10/2015 [ 1 ]
How many structures by NMR ?
Andrew Torda 26/10/2015 [ 2 ]
0
100
200
300
400
500
600
700
800
900
n structures
sizes of NMR structures in protein data bank
0
200
400
600
800
1000
1200
1400
1600
1800
25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450
n structures
n residues Andrew Torda 26/10/2015 [ 3 ]
What is coming
Background to NMR – chemistry
Calculating structures
• distance geometry
• problems with structures
For chemists: no
• chemical shifts
• 2D and higher
• residual dipole coupling, spin labels
• …
Andrew Torda 26/10/2015 [ 4 ]
History
Younger field than X-ray
• 1 ½ Nobel prizes (Ernst, Wüthrich)
First real protein structure about 1985 or 1986
Andrew Torda 26/10/2015 [ 5 ]
NMR from our viewpoint
A way to get structures - our focus
Can provide information on
• dynamics, stability
• interactions (other proteins, small molecules)
Overview – how we get coordinates
• protein in solution
• record spectra
• assign peaks to 1H, 13C, 15N nuclei
• record some more spectra
• distance information (mostly)
• some internal angles
• reconstruct structure
Andrew Torda 26/10/2015 [ 6 ]
Nuclei have spin
• have a charge and act like magnets
• put them in a field and they will align with it
• now apply a magnetic field
• they "precess" around the field
• two possible states
Andrew Torda 26/10/2015 [ 7 ]
or maybe B0
ν
B0
B0 is applied field ν speed of rotation (many MHz / 106 Hz)
μ
Do nuclei like fighting the field ?
Is a nucleus really happy facing the wrong way ?
• what if we push it the wrong way ?
• wants to get to low energy state – emits a photon
Andrew Torda 26/10/2015 [ 8 ]
photon
What NMR records
Andrew Torda 26/10/2015 [ 9 ]
B0
put in energy
B0
turn on a field
some nuclei not doing much
applied field some align
let them relax
Important nuclei (spin ½)
• but the natural isotopes are 12C and 14N
• (usually) these isotopes require labelling
• Proteins
• 1H, 13C, 15N
Andrew Torda 26/10/2015 [ 10 ]
nucleus sensitivity notes 1H 1 cheap and natural
13C 1.6 × 10−2 expensive, but only 1% of natural abundance
15N 10−3 not cheap, 0.4 % natural abundance
31P 7× 10−2 DNA and other PO4 chemistry, less protein
NMR for us
• You get a spectrum (1D, 2D, ..)
• Where are the peaks ?
• For chemists – not this course
• We care about structural information
• This nucleus affects that nucleus
• (field splitting, relaxation, …)
• Can be related back to structure
Andrew Torda 26/10/2015 [ 11 ]
To calculate structures ?
1. distance information
Andrew Torda 26/10/2015 [ 19 ]
2. dihedral / torsion angle information
Distance information / the NOE
Most important (NOE = nuclear overhauser effect)
• an effect which depends on how close in space nuclei are
• NOE ∝ 𝑟−6
• usually only up to about 5 - 6 Å
Story
• two spins' dipoles interact
• cross relaxation phenomenon
Andrew Torda 26/10/2015 [ 20 ]
red relaxing (jumping to lower energy) affects black
Other structural information
• NOE – information about short ( < 5 or 6 Å) distances
• there is more – angles
• mainly J coupling
Andrew Torda 26/10/2015 [ 21 ]
N Cα
H H
N Cα
H
H
cis < 6 - 7 Hz trans ~ 10 Hz
Amide NH to Hα coupling
phi φ
𝐽𝐻𝛼𝑁𝐻
3JHNα coupling
formalised as
𝐽𝐻𝑁𝛼 = 6.4 cos2 𝜃 − 1.4 𝑐𝑜𝑠𝜃 + 1.93
Problems…
Andrew Torda 26/10/2015 [ 22 ]
Where do 6.4, 1.4, 1.9 come from ?
Do not learn for Klausur
0
2
4
6
8
10
-180 -120 -60 0 60 120 180
J (Hz)
φ°
3J coupling curve
from Pardi, A, Billeter, M and Wüthrich, K, J. Mol. Biol. 180, 741-751 (1984)
Amide NH to Hα coupling
• can help distinguish α from β
• not always seen (exchange / motion)
• NH not always present
• other angles ?
• other vicinal protons
• Cα to Cβ
Andrew Torda 26/10/2015 [ 23 ]
-180
-120
-60
0
60
120
180
-180 -120 -60 0 60 120 180
φ phi
ψ psi α
β
Problems with J-coupling
1. we have a formula
𝐽HN𝛼 = 6.4 cos2 𝜃 − 1.4 cos 𝜃 + 1.9 3
Measure 𝐽, solve for 𝜃
• Most of the time, there is more than one solution
• Only use big 𝐽 values
Andrew Torda 26/10/2015 [ 24 ]
0
2
4
6
8
10
-180 -120 -60 0 60 120 180
J (Hz)
φ
3J coupling curve
2. dynamics & errors in J measurement more serious than they appear ! look around −90˚
Practical NMR
We have some basic methods
Real NMR
• more techniques
• 2D and more
• identifying specific kinds of atom
• spreading peaks out
Andrew Torda 26/10/2015 [ 25 ]
Information summary
phenomenon assignments structure
chemical shift important not much used not in Folien
spin-spin (J) coupling
important torsion angles
NOE important distances
Andrew Torda 26/10/2015 [ 26 ]
More spectroscopy
• filtering according to chemistry, atom types
• n-dimensional methods
Structural information
• labels for broadening / shifting peaks
• orientation of bonds to reference ..
Structures from NMR data
Available information
• distances
• short (5 to 6 Å)
• incomplete
• some dihedral / torsion angles
• does this define a structure ?
• strictly no
Coming
• distances in 2D and 3D
• Distance geometry – two versions
Andrew Torda 26/10/2015 [ 27 ]
Determining distances (ideal)
• 2 points 1 distance
• 3 points 3 distances…
• think of 3Natom distances
• remember Natom ≈ 10 or 20 Nres
Andrew Torda 26/10/2015 [ 28 ]
i j dij
dij
dik
dik
i
k j
Underdetermined distances
Think in terms of triangles …
• dik < 6 Å, djk < 6 Å
• where is k ?
A few more distances…
• more and more distances are useful
Andrew Torda 26/10/2015 [ 29 ]
i j
i j
Impossible distances
No overlap ?
• experimental error
• nowhere for k to go
Andrew Torda 26/10/2015 [ 30 ]
i j
Real data
For N residue protein, maybe 5 Nres or 10 Nres
• want more like 3Natom (30 – 60 Nres) distances if perfect
• needs much more data…
• lots of chemical data
Mission
• gather all experimental data
• mix in chemical data
• make all distance information as tight as possible
• put an upper bound on the distance between every pair of points
• put a lower bound on every distance (less important)
• somehow generate coordinates
• start with toys and triangles
Andrew Torda 26/10/2015 [ 31 ]
Structures from distance information
Start in two dimensions..
• ein freundliches Dreieck
• 𝑑𝑖𝑗 = 11 𝑑𝑖𝑘 = 13 𝑑𝑗𝑘 = 16
• fix 𝑖, put 𝑗 on 𝑥-axis and make coordinates
• solve analytically
Andrew Torda 26/10/2015 [ 32 ]
11 13
16
i
k
j
Underdetermined data
• 𝑑𝑖𝑗 = 11 𝑑𝑖𝑘 = 13 𝑑𝑗𝑘 = 12 – 20
• more like NMR data
• unique solution ?
• no
Andrew Torda 26/10/2015 [ 33 ]
11
13
i
k
j
i
11
j k
13
Impossible data
distance too big 𝑑𝑖𝑗 = 11 𝑑𝑖𝑘 = 13 𝑑𝑗𝑘 = 25
distance too small 𝑑𝑖𝑗 = 11 𝑑𝑖𝑘 = 13 𝑑𝑗𝑘 = 1
no 3D structure
Andrew Torda 26/10/2015 [ 34 ]
13
j k
i
11
?
11
13
j
k
i
?
Gathering data
• add in chemistry
• use to get more
• mix chemistry + measurements
• what comes easily from chemistry ?
Andrew Torda 26/10/2015 [ 35 ]
Gather as much data as possible
Simple, geometric information
• bonds – standard
• angles – standard
• simple distances from bond angles
• dihedral / torsion angles
𝑑ℎ𝑘2 = 𝑑𝑖𝑗 − 𝑑ℎ𝑖 cos 𝜃ℎ𝑖𝑗 − 𝑑𝑗𝑘 cos 𝜃𝑖𝑗𝑘
2+ 𝑑ℎ𝑖 sin 𝜃ℎ𝑖𝑗 − 𝑑𝑗𝑘 sin 𝜃𝑖𝑗𝑘 cos 𝜏ℎ𝑖𝑗𝑘
2
+ 𝑑𝑗𝑘 sin 𝜏ℎ𝑖𝑗𝑘2
set 𝜏 = 0
• minimum 𝜏 = 𝜋
• maximum
Andrew Torda 26/10/2015 [ 36 ]
text book
N Cα
H
H
θ
ℎ
i j
𝑘
𝜏 𝜃ℎ𝑖𝑗
How to get more distance information
• impose some distance limits generally
• intuitively
• stretch out a protein and there is a limit to length
Andrew Torda 26/10/2015 [ 37 ]
N Cα
H
H
?? Can one formalise this ?
More general / triangle inequality
What limits can be worked out ?
upper bound 𝑑𝑗𝑘 ≤ 𝑑𝑖𝑗 + 𝑑𝑖𝑘
lower bound
𝑑𝑗𝑘 ≥ 𝑑𝑖𝑗 − 𝑑𝑖𝑘
Andrew Torda 26/10/2015 [ 38 ]
j
k
𝑖
?
j k
𝑖
?
Where to use triangle inequality
One could avoid some ugly trigonometry
Andrew Torda 26/10/2015 [ 39 ]
N Cα
H
H
N Cα
H
H
N Cα
H
H
more general
H H H C
5 Å
implied 6 or 7 Å
Most general triangle bound inequality
Triangle bound should be satisfied by any three points
• chemists
• triangle bound smoothing
• informatik
• all points shortest path problem
Andrew Torda 26/10/2015 [ 40 ]
3
2 3
10
5
3
2 3
10
5
All points shortest path (Floyd)
Andrew Torda 26/10/2015 [ 41 ]
A B C D E A 4 B 3 5 C 2 10 D 3 E
A B C D E A 4 max max max B 3 5 max C 2 10 D 3 E
3
2 3
10
5 A C
D E
B 4
Bound smoothing / Floyd
Andrew Torda 26/10/2015 [ 42 ]
for (k = 0; k < n_last; k++) for (i = 0; i < n_last; i++) for (j = 0; j < n_last; j++) if ij > ik + jk ij := ik + jk
Running time
O(n3)
A B C D E A 4 7 9 12 B 3 5 8 C 2 5 D 3 E
A B C D E A 4 max max max B 3 5 max C 2 10 D 3 E
3
2 3
10
5 A C
D E
B 4
Distance matrix so far
We can build a distance matrix of upper limits
• consistent with all bonds and angles and other information
Can do the same for lower bounds
• every pair of atoms
• invent some lower bound (atomic radii)
Andrew Torda 26/10/2015 [ 43 ]
Does this define a structure ?
Almost certainly not
• still no way to get to a 3D model
From distances to coordinates
How would you build coordinates from distances ?
• stepwise ?
• error prone, errors add
• history
• early 80's
• methods which are tolerant of errors
• metric matrix method
Andrew Torda 26/10/2015 [ 44 ]
Metric matrix method
• get best upper bounds
• get best lower bounds
• guess distances between
→ trial distance matrix
• convert to centre of mass matrix (metric matrix)
• magic conversion to coordinates
• if metric matrix has three positive eigenvalues
• error free coordinates
real coordinates
• lots of errors
• initial coordinates not healthy
• refine
Andrew Torda 26/10/2015 [ 45 ]
Metric matrix method
• get best lower bounds + upper bounds
• guess distances between
→ trial distance matrix
• repeat n times
• get n guesses
• some OK, some bad
• repeat until you have 20 or 100 OK structures
• OK = agrees with experimental data + chemically OK
Andrew Torda 26/10/2015 [ 46 ]
Chirality
2D version
• can *not* be rotated on to each other
• can not be distinguished by distances
3D
• chirality is random
• problem ? no
• flip all coordinates and check
Local chirality …
Andrew Torda 26/10/2015 [ 47 ]
11 13
16
11 13
16
Overall / Local chirality
overall chirality
local chirality
• some points correct
• some wrong
• If you invert a site, will damage other parts of structure
Andrew Torda 26/10/2015 [ 48 ]
The Optimisation problem
Find the coordinates that put atoms so they agree with experimental data
• cost 𝑐 is 𝑟𝑖 − 𝑟𝑖𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 2
𝑖 for each measured distance 𝑟
Maybe we do not work directly with atoms or coordinates 𝑟
work with angles
Andrew Torda 26/10/2015 [ 49 ]
Distances and angles
One angle is easy
Andrew Torda 26/10/2015 [ 50 ]
angle
distance
longer distances depend on several angles
Distances and angles
Each angle affects many distances
What does one know ?
• simple optimisation will not work
Andrew Torda 26/10/2015 [ 51 ]
Optimisation Strategy
Start
• concentrate on distances with few angles in between
• shorter distances become correct
Add in more distances
• re-optimise
Add in more distances
• …
Andrew Torda 26/10/2015 [ 52 ]
Variable target function
Work with torsion angles
Andrew Torda 26/10/2015 [ 53 ]
N H
C H
O
C H 3
H N H
C H
O
C H 2
O H
N H
C H
O
C H O H C H 3
N H
C H
O
C H 2 C H
N H
C H C H
C H
C H
N H
C H
O
C H O H C H 3
N H
C H
O
C H
C H 2
O
O H
O H 2
1st step
2nd step
3rd step
ideas from Braun and Gō, 1980s
Stepwise variable target function method
• Collect experimental data
Andrew Torda 26/10/2015 [ 54 ]
• Sort according to distance in sequence
distance in sequence
residue 1
atom 1
residue 2
atom 2
distance in space (Å)
1 5 Hα 6 HN 4.0
0 8 Hα 8 Hγ 4.4
80 2 Hα 82 HN 4.5
2 3 Hα 5 Hγ 5.0
1 7 Hβ 8 Hγ 3.8
0 3 Hα 3 HN 5.0
Stepwise variable target function method
distance in sequence
residue 1
atom 1
residue 2
atom 2
distance in space (Å)
0 8 Hα 8 Hγ 4.4
0 3 Hα 3 HN 5.0
1 5 Hα 6 HN 4.0
1 7 Hβ 8 Hγ 3.8
2 3 Hα 5 Hγ 5.0
…
80 2 Hα 82 HN 4.5
… …
Andrew Torda 26/10/2015 [ 55 ]
Stepwise variable target function method
distance in sequence
residue 1
atom 1
residue 2
atom 2
distance in space (Å)
1st 2nd 3rd … later
0 8 Hα 8 Hγ 4.4
0 3 Hα 3 HN 5.0
1 5 Hα 6 HN 4.0
1 7 Hβ 8 Hγ 3.8
2 3 Hα 5 Hγ 5.0
…
80 2 Hα 82 HN 4.5
… …
Andrew Torda 26/10/2015 [ 56 ]
Hope..
error
error
conformations
error
1st step
full surface
later step
global optimum
Andrew Torda 26/10/2015 [ 57 ]
Variable target function vs metric matrix
Metric matrix versus variable target function
• proponents of both
variable target function probably more popular
• no problems with chirality
Andrew Torda 26/10/2015 [ 58 ]
Real implementations of distance geometry
• not small programs
• Input ?
• list of protein sequence
• set of distances
• most of code
• libraries of standard amino acids
• code to do geometry and work with standard geometries
• other information
• angle restraints
• convert to distances for metric matrix
• natural for variable target function
Andrew Torda 26/10/2015 [ 59 ]
Output from programs
Structure impossible ?
• program dies or
• best possible solution
Structure not determined ?
• set of possible conformations (10 to 100 )
Andrew Torda 26/10/2015 [ 60 ]
example 1sm7
Lots of models in a PDB file
• big difference compared to X-ray coordinates
• typical
• ends (C- and N-termini) badly defined
• loops poorly defined
• spectroscopists say this reflects mobility
• problems with many models
• difficult to work with
• arbitrary which to select for calculations
• averaging usually not a good idea
• Is this the absolute truth ? No.
• number of models arbitrary
• different methods (programs /details) give different results
Andrew Torda 26/10/2015 [ 61 ]
Finished with making coordinates ?
• structures may not be well defined • can they be improved ? probably
• restrained molecular dynamics (more next semester) • normal MD 𝐸𝑝ℎ𝑦𝑠 𝑟 = 𝑏𝑜𝑛𝑑𝑠 + 𝑎𝑛𝑔𝑙𝑒𝑠 + 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐𝑠 …
• restrained MD 𝐸𝑡𝑜𝑡𝑎𝑙 𝑟 = 𝐸𝑝ℎ𝑦𝑠 𝑟 + 𝐸𝑟𝑒𝑠𝑡𝑟 𝑟
• and… 𝐸𝑟𝑒𝑠𝑡𝑟 = 𝑘𝑖 𝑟𝑖𝑠𝑡𝑟𝑢𝑐𝑡 − 𝑟𝑖
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 2
𝑖
• where i refers to the distance restraint Mission - to minimise Etotal • result ? • structures
• agree with restraints + low energy Andrew Torda 26/10/2015 [ 62 ]
What else can one do with NMR ?
NMR sensitive to dynamics
• is this part of the protein mobile ?
Interactions
• add small molecule – which parts of spectrum change ?
Still more structural information
• residual dipolar coupling
• spin labels
Andrew Torda 26/10/2015 [ 63 ]
Summary
• What information does one have ?
• Is it enough ? Is it consistent ?
• Two methods to generate structures
• Differences in handling chirality
Andrew Torda 26/10/2015 [ 64 ]
Related Documents
